Diplomats and cabinet ministers have grave concerns over the businesses mogul’s praise of Mr Putin and fear he could oversee a major policy shift towards Syrian President Bashar al-Assad.

Sir Alan Duncan, the man tasked with building a relationship with Mr Trump, is also facing embarrassment after it emerged once called him “odious” and prasied a speech where he was dubbed “one of the most malignant figures in modern politics”.

When Mr Tump pulled off his remarkable victory over Hilary Clinton, it was Vladimir Putin who became one of the first world leaders to offer his congratulations.

“Russia is ready and wants to restore full-scale relations with the US,” Mr Putin said. A BBC journalist stationed in Moscow said he could not remember a day foreign ministers had appeared happier.

Across Whitehall, the contrast could not have been starker. Within hours a note circulated to ministers flagged up Trump policies of concern, including his lukewarm stance on Nato.

Chief among the fears in Theresa May’s Government are the glaring differences – if not outright contradictions – in the public positions of the UK and Mr Trump on Russia.

Mr Trump heaped praise on Mr Putin during his election campaign, calling him a better leader than Barack Obama and referencing his strong approval ratings.

Mrs May earlier this year accused the Russian President of overseeing a “blatant breach of international law” over the murder of Alexander Litvinenko, a Putin critic, in Britain.

Over Syria, the incoming American President has repeatedly defended Russia’s military intervention and suggested the two countries can work together to defeat Isil.

Yet just weeks ago Mr Johnson accused Mr Putin’s country of war crimes over the bombing of Aleppo, Syria's besieged capital, and urged protests at Russia’s UK embassy.

And then there is Eastern Europe, where Nato is deploying thousands of troops to counter a Russian military build-up on the border.

Mr Trump refused to support the Nato principle that an attack on one nation is an attack on all during the campaign. Michael Fallon, the Defence Secretary, has pledged Britain will continue to “strengthen” its Nato contributions in a piece for The Telegraph's website..

Such stark policy differences – and their significance for the balance of power across the world – has caused consternation across Whitehall.

The priority now, according to numerous senior sources across Government, is to establish whether Mr Trump’s positions were just ‘campaign rhetoric’ or based on genuine beliefs.

"He’s a guy who thinks he can just conduct foreign policy by being a dealmaker but what would his relationship with Russia be? That’s question number one,” one senior Foreign Office source said.

Another has warned: “There is no hiding the fact that on Russia we have a big problem.”

Access has become part of that problem. Mr Trump’s ever-changing team of aides and advisers infuriated the Foreign Office as they struggled to build relations with the Republican candidate earlier this year.

“People were concentrating more on Bernie Sanders versus Hilary Clinton. Trump was considered a non-starter. Then the dawn of realisation crept up on us,” admitted one senior figure at the time.

David Cameron is understood to have personally ordered better relations be established with Mr Trump as momentum behind the maverick candidate’s White House bid built.

This newspaper understands Mr Johnson, the Foreign Secretary since July, has held three calls with senior Trump allies in 48 hours in a drive to build relationships from a standing start.

Watch | Boris Johnson rejects 'collective whinge-o-rama'

00:35

As well as a call already made public to Mike Pence, the incoming Vice President, he talked to Newt Gingrich and Senator Jeff Sessions – two Washington old hands tipped for senior roles in the Trump administration.

The latter calls, made on Friday night, were both around 10 minutes long and described as “very warm and positive” by a source familiar with the conversations.

It would not have harmed relations that the Americans brought up Mr Johnson’s prolific writing career and mentioned his recent book on Sir Winston Churchill.

Mr Johnson is now planning a trip to the United States before Christmas to meet Team Trump, with aides ready to step in if the Foreign Secretary if waylaid for any reason.

During the trips it is hoped face-to-face talks with Mr Trump’s foreign policy advisers can help establish where his real stance on Russia is before he enters the White House in January.

“After some of the things Trump has said, now we need to establish where he is on Russia,” a Foreign Office source said.

“There is concern about the Nato stance, the Syria stance, the Putin stance. Those were quite heavy comments during the campaign. That is why Boris is having these conversations, so that we can know whether they stand."

However attempts to build bridges have been undermined as the full scale of senior Tory attacks on Mr Trump before his election victory have become clear.

Watch | Barack Obama invites president-elect Trump to the White House

01:26

Sunday Telegraph analysis has revealed that in total nine of the 23 full cabinet ministers made public their opposition to Mr Trump before his victory last week.

Chris Grayling, the Transport Secretary, once said Mr Trump’s views “have no place in a modern society” after he proposed a ban on Muslim immigrants.

James Brokenshire, the Northern Ireland Secretary, suggested the business tycoon’s proposal would fuel “poisonous and pernicious” radicalisation.

Damian Green, the Work and Pensions Secretary, called Mr Trump’s comments about women “offensive” while Justine Greening, the Education Secretary, said they were “utterly crass”.

Sajid Javid, the Culture Secretary, shared a tweet saying Trump supporters were “certified insane”, while Mr Johnson and Mrs May have both also been critical.

The comments will undermine trust amid questions over the “special relationship” after Mr Trump called leaders from nine countries including Ireland, Australia and South Korea before Mrs May.

Yet perhaps the most damaging public criticism of Mr Trump before his victory came from Sir Alan, who as minister of the Americas is tasked with overseeing the UK-US relationship.

Watch | Watch: Key stats from the US election

01:12

While on the backbenches, Sir Alan tweeted praise for a “brilliant” a speech by fellow Tory Zac Goldsmith, adding: “[He] firmly slated the odious Donald Trump.”

Mr Goldsmith’s speech had called Mr Trump “utterly repellent”, “an appalling creature” and “beyond a joke", as well as covering other topics.

But those criticisms are in the past. The Foreign Office’s tone has become one of positivity, friendship and – in Mr Johnson’s dismissal of the “whinge-o-rama” from Europe over Mr Trump – outright support.

Whether those sentiments can withstand the frictions over Russian policy will soon become apparent. On Sunday night, EU foreign ministers will hold an “emergency” meeting over Mr Trump’s victory.

Policy towards Russia will be high on the agenda as anti-Trump protests that have broken out in American cities spread to Berlin yesterday, drawing a crowd of hundreds.

Yet there will be one notable absence – Mr Johnson, who once joked about avoiding New York became of the “real risk of meeting Donald Trump”, but now needs to build ties with the President Elect.

In a bid to align Britain with the US, he has snubbed the crisis meeting. His ability to win influence with Mr Trump, and gain assurances over Russia, could define the fate of the special relationship.